The discovery of government secrets at two locations associated with Joe Biden appears to have produced one big political winner: Donald Trump.

The White House was in rare crisis mode last week as it emerged that lawyers for Biden had found classified material at his thinktank in Washington DC and home in Delaware. At an unusually contentious press briefing, one TV correspondent dubbed the affair “garage-gate”.

The justice department appointed a special counsel to investigate Biden’s handling of classified documents from his time as vice-president. It was a rare setback for an administration that promised to be transparent and scandal-free. It also complicated an investigation into Trump over an ostensibly similar matter.

Another special counsel is already examining the ex-president’s retention of top secret papers at Mar-a-Lago, his Florida estate and club. Although the situations are very different, the nuances and subtleties are likely to be lost in the court of public opinion.

“This may be pure sloppiness on Biden’s part or the Biden team’s part but it doesn’t matter,” said Larry Sabato, director of the Center for Politics at the University of Virginia. “In the public mind, now they will say, ‘Well, a pox on both your houses. You’re both guilty. Shame on you both.’ It’s over.”

The issue could become a continuing political headache for Biden, Sabato added. “It’s just a real distraction. It was totally unnecessary. Every White House makes mistakes and this is a big one they made.”

Despite superficial similarities, the two cases are like chalk and cheese. In January last year the National Archives retrieved 15 boxes of documents from Trump’s home, telling justice department officials they contained “a lot” of classified material.

In August, after prolonged resistance from Trump’s associates to requests and even a justice department subpoena, FBI agents took about 33 boxes and containers of 11,000 documents from Mar-a-Lago, including roughly 100 with classification markings found in a storage room and an office. The FBI warrant showed it was investigating crimes including the wilful retention of national defence information and efforts to obstruct a federal investigation.

The Biden papers are far less voluminous. First it emerged that a “small number” with classified markings had been found in November in a locked closet at the Penn Biden Center thinktank in Washington.

Speaking to reporters on Tuesday in Mexico City, the president claimed that he was surprised when he was informed about them. His lawyers “did what they should have done” when they immediately alerted the National Archives, he said. “I don’t know what’s in the documents.”

Then came news that a second batch of classified documents had been discovered in the garage at Biden’s home in Wilmington, Delaware, and one additional classified page was found in his personal library there. Again, his lawyers informed the archives.

Biden’s offence is seen by analysts as significantly less grave than his predecessor’s. Carl Tobias, a law professor at the University of Richmond in Richmond, Virginia, said: “Given what we know now, it seems that there is a difference in kind, rather than degree, between Trump’s case and Biden’s case.

“For example, quantitatively and qualitatively, Trump’s cavalier and even intentional misconduct regarding the documents, especially those related to national security, appears substantially more egregious than Biden’s apparent neglectful behaviour in not safeguarding certain documents.”

Even so, the White House refused to disclose the content and exact number of the Biden records, how they arrived at his thinktank and home , why they stayed there and why the administration waited more than two months to acknowledge their discovery.

The questions deepened on Saturday when the White House lawyer Richard Sauber revealed that a total of six pages of classified documents had been found in Biden’s personal library in Wilmington; the administration had previously said only a single page came to light there and insisted that the search was “complete”.

White House reporters, who have endured lean times since the wildly norm-busting Trump presidency, have seized on the day-by-day revelations like hungry lions. In the kind of confrontation seldom seen over the past two years, Peter Doocy of the conservative Fox News network asked Biden bluntly: “Classified material next to your Corvette: what were you thinking?”

The president replied: “I’m going to get a chance to speak on all this, God willing, soon, but as I said earlier this week, people – and, by the way, my Corvette is in a locked garage. OK? So, it’s not like they’re sitting out in the street.”

Merrick Garland, the attorney general, selected Robert Hur, a Trump-appointed former US attorney, to investigate the matter. Many legal commentators suggested that a special counsel would not normally have been warranted but the move reflected Garland’s sensitivity to the unique political dynamics.

Trump himself seized on the news, seeking to use it to undermine the investigation into his actions. “It’s over,” he told conservative talk radio host Mark Levin. “When all of these documents started coming out and Biden had them, it really changed the complexion and the intensity that they were showing to me because, you know, what they did is – I don’t say far worse, I did nothing wrong – what they did is not good. What they did is bad.”

In reality, the twist is unlikely to affect the justice department’s decision making with regard to charging Trump. But it could make a criminal case a harder sell to voters, fuelling the scepticism of congressional Republicans and others who have doubted the basis for a viable prosecution.

Jay Town, who served as US attorney in the northern district of Alabama during the Trump administration, told the Associated Press: “I don’t think that it impacts Trump’s legal calculus at all, but it certainly does impact the political narrative going forward. To the extent that the political narrative is a consideration, it does make it harder to bring charges against former President Trump as it relates to the documents seized at Mar-a-Lago.”

The drama is unfolding just after Republicans took control of the House of Representatives eager to target the federal government with accusations of politically motivated prosecutions. On Friday, Jim Jordan, chair of the House judiciary committee, announced an investigation into Biden’s handling of classified documents, particularly what the justice department knew about the matter.

Republicans are also well practised in the political art of false equivalence and “whataboutism”. During the 2016 presidential election campaign, allegations that the Trump campaign was colluding with Russia were effectively neutralised by a controversy over rival Hillary Clinton’s private email server.

The week’s events dealt an unexpected blow to Biden as approval ratings were rising, inflation was slowing and Republicans had just endured a chaotic election for House speaker. They also threw a lifeline to Trump, whose 2024 presidential election campaign made a wretched start. But he still faces myriad investigations into his business affairs and his role in the January 6 attack on the US Capitol.